Question

What is value of x? Enter your answer in the box.

Answer 1

Answer:

$x \ = \ 10$

Step-by-step explanation:

Let point $D$ be the point where the straight line drawn from point $A$ meets the straight line $BC$, it is evident that $\triangle ABD$ and $\triangle ACD$ is similar given that both triangles share the same angle, $\angle BAD \ = \ \angle DAC$. Hence, the ratio of the sides of each triangle is the same. Specifically,

                                              $\displaystyle{\frac{x+4}{8} \ = \ \frac{2x+1}{12}}$.

Performing cross multiplication yields

                                           $12\left(x+4\right) \ = \ 8\left(2x+1\right) \\ \\ \rule{0.15cm}{0cm}12x+48 \ = \ 16x+8 \\ \\ \rule{1.1cm}{0cm} 4x \ = \ 40 \\ \\ \rule{1.3cm}{0cm} x \ = \ 10$.